Projected area is two-dimensional area

Area

Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat...

 measurement of a three-dimensional object by projecting its shape on to an arbitrary plane. This is often used in mechanical engineering

Mechanical engineering

Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. It is the branch of engineering that involves the production and usage of heat and mechanical power for the...

 related fields, specifically hardness testing, axial stress and terminal velocity

Terminal velocity

In fluid dynamics an object is moving at its terminal velocity if its speed is constant due to the restraining force exerted by the fluid through which it is moving....

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The geometrical definition of a projected area is: "the rectilinear parallel projection

Parallel projection

Parallel projections have lines of projection that are parallel both in reality and in the projection plane.Parallel projection corresponds to a perspective projection with an infinite focal length , or "zoom".Within parallel projection there is an ancillary category known as "pictorials"...

of a surface of any shape onto a plane". This translates into the equation:


where A is the original area, and is the angle between the normal to the surface A and the normal to the arbitrary plane onto which we project. For basic shapes the results are listed in the table below.

Projected area for basic shapes

Shape	Area	Projected area
Flat rectangle
Circular disc
Sphere